Hydraulic Arbor Design

2 · Analysis — turn the knobs, watch it respond

4 · The sleeve in 3-D — von Mises field on the deformed body

Drag to orbit · scroll to zoom. The cutaway shows the through-wall field; the skins carry the face stresses. Deformation exaggerated ×65. Peak vM 27,919 psi vs σ_y(sleeve) 95,000 psi — re-solved live at every knob turn.

5 · Principal-direction field — σ₁ arrows through the wall

Drag to orbit · scroll to zoom. Each arrow lies along the local σ₁ (most-tensile principal) direction; length tracks |σ₁| and color its signed level — tension vs compression. Hoop rings where ring stretch rules; near welds and band edges the bending + transverse-shear tilt rotates the arrows into the wall. Geometry undeformed. σ₁ spans 10,484 … 27,322 psi — re-solved live at every knob turn.

Notes

Engine: N-layer compound-cylinder solver (Lamé thick-wall, multi-interface coupled solve via Eigen, compiled to WebAssembly). Contact is unilateral — an interface flagged clearance has separated under the given loads/temperatures. Safety factor = material yield ÷ peak von Mises (set σ_y via the material). Suggested-fit limits use the ISO 286 tables from the source workbook; validated to <0.1%.
Elastic-plastic analysis (opt-in, in Loads & options) runs an incremental flow-theory solve (von Mises J2 or Tresca; perfectly-plastic or with linear strain hardening set per material via a tangent modulus E_t) for the true post-yield state: it caps stress at the yield surface, grows a plastic zone from the bore, relieves the contact pressure, and reports the residual stress and the gross-yield (limit-load) margin — the factor by which the whole load can scale before a member becomes fully plastic, found numerically. The standard first-yield safety factor remains a valid conservative basis; the limit-load margin governs once a member is allowed to yield locally. A fit that exceeds gross-yield collapse is flagged.
The hardening model chooses how a hardened material re-yields when the operating loads are removed: isotropic grows the yield surface (reverse yield delayed by the full 2·(σ_y+E_t-growth) span), while kinematic translates it — the Bauschinger effect, so reverse yield follows a fixed 2·σ_y swing and re-yields earlier, eroding the locked-in autofrettage compression. The two coincide on monotonic loading and whenever E_t=0; the difference appears only on reverse yielding, which the panel flags. Kinematic/mixed applies to the von Mises criterion (the standard Prager back-stress calibration).

How It Works

A hydraulic arbor is an interference fit you can switch on and off. A thin sleeve is welded to the body around an annular oil chamber; a setscrew piston (or a factory charge) pressurizes the trapped oil and the sleeve bulges elastically as a free ring — a few hundredths of a millimetre is plenty. That motion closes the small fitting clearance to the part, and every bit of pressure past lift-off becomes contact pressure at the grip; friction riding on that pressure holds the torque, exactly the thick-wall (Lamé) mechanics of a press fit. This page runs the same N-layer engine as the Press-Fit Designer with the oil film as one more unilateral interface — OD grip puts the chamber under the sleeve so it expands into a workpiece bore (expanding arbor / mandrel); ID grip puts the chamber outside the sleeve so it contracts onto a tool shank (expansion chuck). Because the ends are welded, the oil is a closed spring: temperature and outside squeeze re-solve its operating pressure through the trapped volume.

Key Components

• Body — the arbor or chuck core; carries the galleries and the charge screw. Stiff by design so the sleeve does the moving.
• Expansion sleeve — the thin wall that does the work; welded or brazed at both ends to seal the chamber. Wall thickness is the key trade: thin lifts far but yields early (run the Wall study).
• Oil chamber & galleries — the annular gap plus drillings and the screw bore; their total volume is the “Oil volume” input and sets the oil-spring stiffness of the sealed system.
• Charge screw / piston with seals — sets the charge pressure; on toolholders it is the wrench flat on the side of the chuck.
• The gripped surface — workpiece bore over the sleeve (OD grip) or tool shank inside it (ID grip). Its tolerance must land inside the sleeve’s lift window — h6/g6-class fits in practice.

Common Configurations

• Expanding arbor / mandrel (OD grip) — locates gears, rings and bearing races on their bores for turning, grinding and inspection; runout in single microns.
• Hydraulic expansion toolholder (ID grip) — grips drill, reamer and endmill shanks; the oil film also damps vibration, improving surface finish and tool life (SCHUNK’s TENDO line is the classic example).
• Double-sleeve locking bushings — one charge grips ID and OD at once for hub-to-shaft connections; that case has its own sheet: Hydraulic Bushing Design.
• Workholding fixtures — multiple small arbors plumbed to one supply for clamping thin-wall parts without distortion.

Advantages and Limitations

• Advantages: micron-level concentricity and repeatability; part change in seconds with no press or oven; uniform all-around pressure that does not lobe thin rings; the oil film damps chatter; grip is adjustable and fully reversible.
• Limitations: the part tolerance must sit inside the lift window (≈0.01–0.03 mm on Ø for typical sleeves) — a sloppy bore never seals the grip; a sealed charge loses pressure as it warms less than it gains squeeze, but hot spindles do walk the grip (check the Fit-vs-temperature tab); the thin sleeve sets a hard pressure ceiling at yield (use Max @ SF); and static rigidity is below a shrunk joint of the same size — heavy interrupted cuts favor shrink-fit holders.

References & further reading

• SCHUNK — TENDO hydraulic expansion toolholders — the standard ID-grip implementation and its application data.
• ETP Transmission — hydraulic hub–shaft connections and expanding mandrels (OD grip).
• Wikipedia — Interference fit — the underlying friction-joint mechanics.
• Wikipedia — Cylinder stress (Lamé equations) — the elasticity this engine solves.
• Wikipedia — Fluid bearing — background on pressurized films between surfaces.

Disclaimer

Recommendations on application design and material selection are based on available technical data and are offered as suggestions only. Each user should make their own tests to determine the suitability for their own particular use. Standards Applied LLC offers no express or implied warranties concerning the form, fit, or function of a product in any application.

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